Retarded potentials and Time Domain Boundary Integral Equations, a road map

This is my little contribution to the analysis of boundary integral equations for the transient wave equation (acoustic, elastic, electromagnetic) and their discretization, using Galerkin methods in space and Convolution Quadrature in time. It's the result of almost five years of work, starting from very detailed classnotes on the necessary background (Laplace transforms of causal distributions, convolution operators, the Bamberger-HaDuong theory of TDBIE) and moving to new grounds (use of semigroup theory for TDBIE).

Related materials

  • Code for your own 2-dimensional acoustic and elastodynamic simulations can be found at the deltaBEM site.
  • I keep a file with errata here.
The book